Means and method of lapping the curved surface of gears and the like



I July 11, 1939. w KLQMP 2,165,386

IEANS AND METHOD OF LAPPING THE GUBVED SURFACE CF GEARS 'AND THE LIKE Filed July 11, 1934 '4 Sheets-Sheet 1 J7" w 44' 5, G1 N i 8 4?! I 4%,- I

J A 7 r J g5 z? 24 4Ialw/ 5 I I 1?} 2/ 20-" I INVENTOR TTORNEYS y 11, 9 A. w. KLOMP 2,165,386

MEANS AND METHOD OF LAPPING THE CURVED SURFACE OF GEARS ANlj THE LIKE' Filed July 11, 1934 4 Sheets-Sheet 2 INVENTOR MW fwd-0 TTQRNEYS Jul 11, 1939. A P 2,165,386

MEANS AND METHOD OF LAFPING THE CURVES SURFACE OF GEARS AND THE LIKE Filed July l1, 1934 4 Sheets-Sheet July 11, 1939. A j L gP 2,165,386

MEANS AND METHOD OF LAPPING THY; CURVED SURFACE OF GEARS AND THE LIKE Filed July 11, 1934 4 Sheets-Sheet 4 Patented July 11, 1939 UNITED STATES 2,165,386 I MEANS AND METHOD OF LAPPINGI THE CURVED SURFACE OF GEARS AND LIKE THE

' Alfred W. Klomp, Detroit, Mich., assignor, by mesne assignments, to The Carborundum Company, Niagara Falls, N. Y., a corporation of Delaware Application July 11, 1934, Serial No. 734,609

16 Claims.

This invention relates to a means and method of finish-grinding, honing, or lapping curved surfaces, and more particularly to the line contact lapping of curved, generated surfaces, such 5 as the tooth flanks or spur, helical, herringbone (or other multiple gears) and compound gears of both the external and the internal types.

The principal objects of the invention are: (1) to provide a lapping action which will be uniform over the entire face of the curved surface, and will, at the same time, lap said surface to a geometrically correct shape, (2) to perform a plurality of lapping operations on the same workpiece at the'same time and thereby reduce production time, (3) to simultaneously perform lapping operations on a number of workpieces which are integrally or otherwise connected together,

(4) to permit such a type of lapping to be effected by movements of the lapping member in two directions only, (5) to make possible the e1imination of the ordinary messy feeding of abrasive to the lapping member and the likelihood of these particles becoming imbedded in the workpiece,

. and, (6) to correct discrepancies in tooth form 25 resulting from faulty previous production operations performed on the workpieces. Numerous other collateral objects of the invention and practical solutions thereof are disclosed in detail in the herein patent specification, wherein:

30 In the accompanying drawings:

Fig. l is a top plan of a machine for lapping spur or helical gears in accordance with the present invention.

Fig. 2 is a side elevation thereof. I

Fig, 3 is a fragmentary, enlarged, plan view of one of the lefipingmembers, shown in Figs.

1 and 2. a

Fig. 4 is a fragmentary, enlarged, plan view of a modified form of lapping member for finishing spur gears.

Fig, 5 is a diagrammatic, horizontal sectional view through the workpiece and lapping members of Figs. 1 and 2.

Fig. 6 is an enlarged perspective view of one of the teeth of the workpiece of Figs. l, 2 and 5, showing diagrammatically the initial lapping operations performed thereon.

Fig. 7 is similar to Fig. 6 but shows diagrammat ically the complete lapping operations performed on each tooth of said workpiece. I

Fig. 8 is a diagrammatic, horizontal-sectional View through a workpiece and its lapping members showing the arrangement for curing consistent discrepancies of the angular type in the workpiece as received by the final lapping machine which constitutes the present invention.

Fig. 9 is an enlarged, perspective view of one of the teeth of the workpiece of Fig. 8 showing diagrammatically the complete lapping operation performed on said workpiece for the purpose of correcting consistent discrepancies of the angular type.

Fig. 10 is a diagrammatic, horizontal-sectional view through a workpiece and its lapping members showing the arrangement for curing consistent discrepancies of the bevel type in the workpiece.

Fig. ll is a diagrammatic, horizontal-sectional view through a lapping set up in which one lapping member is used to lap two workpieces simultaneously.

Fig. 12 is an enlarged perspective of a gear tooth showing, graphically the direction of lapping caused initially thereon by rotation only when the line of rolling contact is oblique.

Fig. 13 is an -enlarged perspective of a gear tooth showing graphically the direction of lapping caused. initially thereon by rotation and longitudinal movement in a rearward direction of theworkpiece when the line of rolling contact is oblique, such a rearward movement counteracting to some extent the angularity of the lapping action. I

Fig. 14 is an enlarged perspective of a gear tooth showing graphically the ratio of intensity of lapping caused initially thereon by rotation only when the line of rolling contact is oblique.

Fig. 15 is an enlarged perspective of a gear tooth showing graphically the distribution of lapping caused thereon when said lapping action has been completed.

Fig. 16 is a diagrammatic plan view of the invention as applied to the lapping of a cluster type of gear.

Fig. 17 is a diagrammatic, horizontal-sectional view of the invention as applied to the lapping of a herringbone or other multiple gear whether the teeth of the respective gears are staggered or in line.

Fig. 18 is a diagrammatic, vertical, transverse sectional view thereof.

Fig. 19 is a diagrammatic, horizontal-sectional view of the invention as applied to the lapping of spur or helical gears by an internally toothed lapping member.

Fig. 20 is a diagrammatic, horizontal-sectional view of the'invention as applied to the lapping of an internal gear.

Similar characters of reference indicate like parts in the several figures of the drawings.

Lapping spur o'r helical gears Figs. 1 and 2 illustrate one form of machine for "finish-grinding or lapping a spur or] helical gear. Said machine comprises a base having its upper portion provided with a medial, longitudinal slide 2| upon which a carriage 22 is adapted to be re'ciprocated by a suitable link 23 and lever 24, the latter being pivoted to the base 20 at 25 and being preferably actuated from a suitable source of power. The longitudinal movement of said carriage may, if desired, be limited by suitable stop pins 26 and 21 which project upwardly from said base 20 and engage alternately with opposite sides of said lever 24.

Formed at the rear (left) end of said carriage 22 is a head post 28 carrying a head center 29. The latter may, if desired, be rotatably mounted in said head post on an anti-friction bearing 30.

Formed centrally and longitudinally in said carriage 22 is a slide 3|, upon which is slidably mounted a tail stock 32. Said tail stock is adapted to be moved to any desired longitudinal position on said slide and hence on said carriage 22, and then held firmly in place by a clamp 33.

Formed centrally on said tail stock 32 is a tail post 34 in which is arranged a longitudinal tail center 35. The latter is at all times axially in line with the head center 29 and may, if desired, be rotatably mounted in said tail post on an anti-friction bearing 36.

Adapted to be arranged between said head and tail centers-29 and 35 is a mandrel 31 which is provided with a suitable shoulder 38 and clamping nut 39 to enable the workpiece 40 to be coaxially secured thereon. In this particular case this workpiece 40 is a plain spur gear, and it is to be assumed thatthis spur gear has already been rough machined and then heat treated.

From the foregoing it will be seen that the spur gear workpiece M is free to rotate on its axis and can, at the same time, be reciprocated axially.

Secured to the top face of the base 20 at the rear end thereof are a pair of swivels M, Ma each of which is angularly adjustable about a vertical axis. This angular adjustment is facilitated by theprovision of suitable arcuate scales 42,!l2a secured to the respective swivels and cooperating with suitable companion indicators or pointers #3, 63:; secured to the base 20. When said swivels have been moved to their desired angular positions, they are secured in position by suitable clamp bolts fi l, itan On the swivel M is arranged a pair of bearings 55, 45 in which a horizontal shaft at is journaled.

Similarly, the swivel Ma is provided with a pair of bearings til, 37 in which a horizontal shaft i8 is journaled. Said shafts #36 and as l ie preferably in the same horizontal plane as the axis of the workpiece ill, but, in the position shown in Figs. 1, 2 and 5, are each preferably disposed in said plane at the same angle A (see Fig. 5) relatively to the axis. of said workpiece" M.

At the front end of the shaft i6 is mounted a driving lapping member 59, while at the front end of the shaft 58 is mounted a driven lapping member 49a which is preferably identical in shape and size to the driving lapping member &9. In the preferred form of the invention, these lapping members consist of a bonded abrasive material which is suitably moulded or cut to shape.-

eral rows of gear teeth 50 and 50a. The opposite faces of each of said teeth are denominated by the numerals 5i and 5| and 5Ia and 5la' respectively. Said teeth 50 and 50a are of such shape and configuration that the shape of each of their corresponding lapping members 49 and 49a is that of a special form of bevel gear, which enables them to'mesh in'a special andunorthodox manner with the teeth of the workpiece.

The one shaft 46 has centrally secured thereto a suitable pulley wheel 52 which is engaged by and driven by an endless drive belt 53. The other shaft 48 has centrally secured thereto a brake drum 54 which is encircled by a flexible and suitably lined brake band 55. This band is suitably prevented from rotating with said brake drum 54 by the provision of a bracket 56 which is secured at'its upper end to said brake band 55 and at its lower end to the base 20. The amount of tension exerted by said brake band 55, upon its brake drum 54 is suitablyadjusted by an adjusting nut 51. If the energy absorbed by said brake becomes excessive it may be cooled by a stream of cold water, or in any other of the usual and well known manners.

By reason of this braking action which restrains rotation of the shaft 48 together with its driven lapping member 49a, and by reason, furthermore, of the fact that the other or driving lapping member 49 is driven by the belt 53, it follows that while the workpiece 40 is being rotated, its tooth faces are subjected to'a rolling and rubbing movement exerted by the successive bonded-abrasive teeth of said lapping members 439 and 49a.. This causes a lapping action between said bonded abrasive teeth of said lapping members and the teeth of the workpiece 40.

It is possible to lap the teeth of the workpiece I MI by the use of metal lapping members supplied firmly imbedded in the metal of the workpiece.

This'latter is manifestly very deleterious. For these reasons the lapping action obtained by the use of lapping members constructed of bonded abrasive material, such as shown in the present disclosure, is preferred.

The chief features of the present invention are a consequence of the shape of the teeth of the lapping members 459 and dim, and of their an- I. gular axial disposition relativelyto the axis of the workpiece 50. The co-relation of these features is as follows:

Referring particularly to Figs. 5-7, the line 58 represents the normal line of rolling contact'of the workpiece or gear 58, i. e., the line at which there is no rubbing action, but only rolling contact, between it and its mated working gear (not the lapping member), whenin actual operation. Ordinarily, this line intersects the pitch circle (not shown) both in the case of involute and cycloidal gears and also in other types of gears. If it is assumed that in practice the line of rolling contact has some width due to deflection of the metal under running pressure so'as to constitute in effect a narrow elongated area of rolling contact, the medial longitudinal line of said area constitutes the normal medial line of rolling contact.

' the latter is in the center of its reciprocatory' I In gear lapping operations as heretofore practiced, the line of rolling contact between the lapping member and the workpiece was similar to the normal line of rolling contact 58, in that it was situated in a plane parallel to the axis of the workpiece. The result of this was that this line of rolling contact 58 on each tooth face of the workpiece was not lapped at all as far as rotation only was concerned. It consequently was necessary to provide one or more additional movements of the lapping membersrelatively to the workpiece (such as longitudinal and transverse) to enable a lapping action at this normal line of rolling contact 58 to be effected.- But, even with such a combination of movements, the lapping action over the whole tooth face was not satis-- factory, because its action was not properly distributed over said tooth face. In particular, the

total effective lapping action was greater farther away from the normal linof rolling contact 58 than it was near said normal line of rolling contact. Hence, the more the workpieces were lapped in such a manner, the more inaccurate the tooth profile became.

In the present invention, when the belt 53 is driven in the direction indicated by the full line arrow of Fig. 1, the tooth face 5| of the driving lapping member 49 bears against the one tooth face 59 of the workpiece 40, the oblique line of rolling contact 68 between said tooth face 5| and tooth face 59 being disposed at an angle with the axis 6| of said workpiece and consequently also at an angle with the normal line of contact 58 (see Figs.5 and 6) of said tooth face 59. Similarly, under these same conditions of power drive and direction of rotation, the tooth face 5|a of the driven lapping member 49a is pressed upwardly by the other tooth face 59' of said work-. piece 40, the oblique line of rolling contact in this case being 60' (see particularly Fig. 6),. If the rolling contact between the lapping member 49 and the workpiece 40 in practice occurs on a narrow elongated area or line having perceptible width as distinguished from a theoretical line without width, the longitudinal medial line of said area constitutes the aforesaid oblique line of rolling contact.

Taking, for the present, however, only the one tooth face 59 0f the workpiece 40 into consideration, the resultant of the lapping due to rotation only is shown diagrammatically in Fig. 14, in which it is seen that the oblique line of rolling contact 60, along which no lapping has occurred, is at an angle to the normal line of rolling contact 58 and intersects the latter at a point of intersection 62. This point of intersection preferably lies midway of the faces of the workpiece 45 when movement, as shown in Figs. 1, 2 and 5. The angle -A between said oblique line of rolling contact 60 and the normal line of rolling contact 58 is illustrated as being the'same as the angle A between the axis 46 of the lapping member 49 (or the axis 48 of the lapping member 49a) and the axis 6| of the workpiece 40. It is, however, not essential that these. two angles be equal to each other, in fact in actual practice they are not equal-to each other.

For any one given longitudinal position of the workpiece, there is only one point 62 on the normal line of rolling contact 58 which is not portion of said normal line of rolling contact 58 receives some degree of lapping action. Likewise every portion of the tooth face 59 receives some degree of lapping action. This action is not as.

drive belt 53 is driven in a. reversed direction as indicated by the dotted arrow of Fig. 1. This causes the driving lapping member 49 to bearwith its rear tooth face 5| against the rear" tooth face 59" of the workpiece 40 on an oblique line of rolling contact 63 (see Fig. 7). Simultaneously, the front tooth face 59 of said workpiece 40 bears against the "front tooth face 5|a of the driven lapping member 49a on an oblique line of rolling contact 63'.

As far as the one tooth face 59 of the workpiece 40 is concerned, it is obvious that it is op- ,erated upon by the front tooth face 5| of the 5 driving lapping member 49 on the oblique line of rolling contact 60, and that when the drive belt 53 is reversed, said tooth face 59 of said workpiece 40 is operated upon by the front face 5| a of the driven lapping member 4911 on the oblique line of rolling contact 63'. While this lapping action is going on as to this front tooth face 59 of said workpiece, the latter is being reciprocated by the lever 24. The consequence is that this front tooth face 59 receives an even lapping action which when complete appears as shown in Fig. 15. The opposite or rear face 59' of said workpiece 48 receives a similar uniform lapping treatment.

When the axes 46 and 48 of the lapping members 49 and 49a are set at an angle with the axis 6| of the workpiece 40, the shape of the teeth of said lapping members will ordinarily resemble the teeth of an ordinary bevel gear in that their outer ends will be tapered as shown in the enlarged fragmentary plan view of Fig. 3. The

- present invention is not, however, confined to lapping members of bevel gear shape, it being obvious that an oblique line of rolling contact may be obtained by a considerable variety of shapes of lapping members. In Fig. 4, for instance, is shown an enlarged, fragmentary plan view of a lapping member having the outermost portions of each pair of tooth faces of each tooth parallel to each other but at an angle to the axis of the the root or innermost portions of each pair of tooth faces of said tooth parallel to the axis of the lapping member. With a lapping member having teeth of such shape, the axis of the lapping wheel'would be disposed parallel to the axis of the workpiece. v

Each of the lapping members has been described herein and is shown in the drawings as having peripheral teeth which are of such shape and configuration that they will mesh properly with the gear teeth of the work piece, and have therewith a line of rolling contact inclined to the normal line of rolling contact of the workpiece with a mating workpiece. Therefore, the lapping member has an operating pressure angle, in relation, for example, to a cylindrical gear meshing therewith, which varies progressively from one end of the tooth flanks or faces to the other. The line of involute action and hence the pressure angle between two mating gears will vary with changes in the center distance of the gears. In the present instance, the center distance between the axis of the workpiece and the axis of the lapping member varies progressively from one side to the other. It follows that the degree of variation in the pressure angle, and of the in-.

form, and the teeth of the lapping member may be considered as being generated on a theoretical base cylinder.

The variation in pressure angle is reflected in the shape or configuration of the teeth of the lapping member. In this connection, it will be noted that the top of each tooth is tapered longitudinally toward the large diameter of the lapping member; that the base of each tooth is oppositely tapered, and that the inclination of the flanks or faces of each' tooth relatively to the radius of the lapping member varies progressively from end to end. g

In actual production, the workpieces 40 go through a number of operations before reaching the finishing or final lapping machines which constitute the present invention. Because of the flow of workpieces uniformly through said previous operations, it frequently happens that there are consistent discrepancies in said workpieces. Such consistent discrepancies are most expeditiously taken care of by so setting the finish lapping machine as to compensate for the same; One way of accomplishing this, in the case of a straight? spur gear I40 having teeth which are substantially straight but are actually disposed at a slight angle to the axis of the spur gear orsymmetrical with respect to the tooth faces I1!!! and I59 of the workpiece I40 and hence the lapping action is also unsymmetrical, the angles 3 and B and the amount of lapping, being adjusted, of course, to suit the angle and the amount of the consistentdiscrepancy in question.

Fig. 10 shows a means of compensating for consistent discrepancies wherethe teeth are of the straight spur gear type but, due to inaccuracies in the previous machining operations, have teeth which are of slightly tapered form. In this case both of the lapping members 249 and 2490 are so disposed that all oflthe inclined ,or oblique lines of rolling contact between said lapping members and the tooth faces of the workpiece 240 are arranged at such an angle as to straighten each tooth on each of its faces and lap its profile so as to be parallel to the axis of the workpiece 240. ,1

Fig. 11 illustrates a method of using a single lapping member 349 to operate simultaneously on two workpieces 340 and 340'.

Figs. 12 and 13 illustrate the direction of the lapping action obtained with the present invention. Fig. 12 shows the direction of lapping due to pure rotation said direction being illustrated piece 440 because of the fact that the axis of the greases lapping member in question is not parallel to the axis of said workpiece. Ordinarily said graph lines 64 are-substantially perpendicular to the oblique line of rolling contact 460 at the points of contact therewith.) Fig. 13 illustrates how these graph lines 64 are warped to form graph line 464 when the workpiece 440 is not only rotated but is also given a small longitudinal component of counteractory (in this case rearward) motion by the lever 24. Therefore, inasmuch as the oblique line of rolling contact 460 moves parallel to the axis of the workpiece 440, it follows that the angle at which the lapping occurs at different points varies considerably as said workpiece is reciprocated. This, too, helps to average up the total effective lapp action over the varioiis portions of the face of the workpiece teeth.

Cluster gears Herringbone and other multiple gears Figs. 17 and 18 illustrate diagrammatically how,

Fig. 18. Such an arrangement permits the mul tiple gear to be finish-lapped in one setup.

Plain spur gears with internal toothed lapping member Fig. 19 illustrates how a plain spur gear II40 can be lapped with'the present invention by the use of an internal toothed lapping member H49. Such a lapping member permits of a number of such spur gears being lapped at the same time .such as that indicated by dotted lines at II49a.

This system is of special advantage in lapping spur gears which in actual use are mated with either an internal gear or one having a similar pressure angle relatively to the pur gear.

Internal gear lapping Power transmission In all the cases thus far described, transmission of power has been carried from a lapping member to 'the workpiece, or vice versa, the fact that power was being transmitted being incidental to the main function of lapping the tooth faces of the workpiece. And in all such cases the line ofrolling contackwas oblique to the pitch surface (generated by the pitch circles) of both said workpiece and said lapping member.

It is obvious, however, that power may be transmitted in exactly this same manner without causing any lapping action, if both the lapping" member and the workpiece are constructed of metal or other non-abrasive material and are fed with a suitable lubricant to reduce the frictional resistance to rotation. Such a power transmission has the distinct advantage of being less noisy than its corresponding conventional gear, not because of thechange, per se, in the line of rolling contact, but as a consequence of the fact that, when said line of rolling contact is made oblique, the time at which difierent transverse sections of the gears come into and go out of contact is altered in a manner somewhat analogous to the engagement of spiral gears.

It should be noted that such a transmission of power with an inclined line of rolling contact is not confined to plain spur gears, but may be used with spiral and bevel gears and even in worm'gears. In the case of the worm gears it would ordinarily be only the worm wheel which would have an unconventional form, whereas in the case of all the other gears either the one or the other or both of the mating gears could have the unconventional shape with an oblique line of rolling contact. In all such cases the line of rolling contact does not lie in the pitch surface of any of the gears but is disposed obliquely to both of said pitch surfaces.

Definitions To prevent any ambiguity as to what is meant by the various terms used in the foregoing specification and in the appended claims, the following precise definitions are deemed to be useful: a

By line of rolling contact is meant the theoretical line on any certain tooth flank of a gear shaped member along :which line no sliding occurs when said member is rotated in mesh with another specific gear-shaped member.

By normal line of rolling contact is meant the theoretical line of rolling contact on any certain tooth flank of a gear-shaped member along which line no sliding occurs when said member is rotated in mesh with another gear-shaped member having the same pitch, the same pressure angle, and the same helix angle.

By point of contact is meant the theoretical, instantaneous point where the tooth flank of one gear-shaped member touches the tooth flank of another gear-shaped member with which it is in mesh.

By cylindrical gears are meant those whose pitch circles all lie in a straight pitch cylinder, such as spur gears, spiral gears, herringbone gears, and gear-shaped splines.

By lap is meant an abrading member, such as a bonded abrasive member or a cast iron or other relatively soft metal member loaded with some suitable abrasive powder.

I claim as my invention:

1. The method of lapping a gear consisting of engaging said gear with a lap, which, when running in mesh with said gear, has a medial line of rolling contact with each successive tooth flank of said gear and abrades said tooth flank above and below said line of rolling contact, said line of rolling contact being disposed obliquely with reference to the normal medial line of rolling 2. The method of lapping a gear consisting of engaging said gear with a lap, which, when rotated in mesh with said gear, has a narrow elongated area of rolling contact with each successive tooth-flank of said gear and abrades said tooth flank above and below the medial line of said area of rolling contact, said medial line of said area of rolling contact being disposed obliquely with reference to the normal medial line of rolling contact of said tooth 'flank with the flank of a similar gear; rotating said gear and lap in mesh; and moving said gear relatively to said lap in a direction inclined to said" first mentioned medial line of rolling contact- 3. The method of lapping a cylindrical gear having a constant pressure angle consisting of meshing said gear for full involute engagement with a gear-shaped lap having a varying pressure angle lengthwise of the lap teeth; and running said gear and lap together while in mesh and with the axes of said gear and said lap relatively inclined in a common plane.

4. The method of lapping a gear having a constant pitch and a constant pressure angle consisting in meshing said gear for full involute engagement with a gear-shaped lap having a varying pressure angle, running said gear and lap together while inmesh and with the axes of said gear and said lap relatively inclined in a common plane; and simultaneously reciprocatably moving said gear relatively-to said lap in a direction parallel to the axis of said gear.

5. The method of lapping a gear consisting of engaging said gear with a. lap adapted to rotate on an axis lying in the same plane as the axis of the gear, the teeth of said gear and lap being of such form that when said gear and lap are rotated in mesh, an instantaneous narrow area of rolling contact is obtained on each successive tooth flank, and the area above and below said area of rolling contact is abraded, the medial longitudinal line of said area of rolling contact being disposed obliquely with reference to the medial longitudinal line of the normal area of rolling contact of the tooth flank when said gear is in mesh with a similar gear, and rotating said gear and said lap while in engagement.

with the other lap, the medial longitudinal lines of said areas of rolling contact intersecting each other between the ends of the tooth flank.

"7. The method of lapping a gear which comprises positioning the gear in meshing engagement with a gear-shaped lap adapted upon rotation of said'gear and said lap to have rolling contact with each successive tooth flank of said gear on a medial line extending substantially across said flank and adapted to abrade said flank above and below said medial line of said rolling contact, running said gear and said lap together while in said meshing engagement, and simultaneously relatively moving said gear and said lap in a direction oblique to said medial line of said rolling contact while maintaining a constant depth of meshing engagement.

8, The method of'lapping a gear which comprises positioning the gear in meshing engagement with a conjugate gear-shaped lap whose axis lies in the same plane s the axis of said gear and whose pressure angle varies relatively to the pressure angle of said gear progressively along each gear tooth flank, said lap being adapted upon rotation to have rolling contact with each suc-' cessive tooth flank of said gear on a medial line extending substantially across said flank and adapted to abrade said flank above and below said line, running said gear and said lap together while in said engagement, and relatively moving said gear and said lap in a direction oblique to the direction of said medial line of rolling contact between said gear and said ,lap while maintaining a substantially constant depth of meshing engagement.

9. The method of lapping a gear which comprises positioning the gear in meshing engagement with a conjugate gear-shaped lap whose axis lies in the same plane as the'axis of said gear and is disposed obliquely relatively thereto and whose pressure angle varies progressively along each gear tooth flank, running said gear I and said lap together while in said engagement,

positioning said gear in meshing engagement with a second conjugate gear-shaped lap whose axis lies in the same plane asthe axis of said gear and is disposed obliquely relatively thereto and whose pressure angle varies progressively along each gear tooth flank but in the opposite direction to that of said first mentioned lap, running said gear and said second mentioned lap together while in said engagement, and relatively moviiig said gear-and each lap in a direction parallel to the axis oi said gear during each engagement.

10. As an article of manufacture, a rotary gearshaped conical lapping member of bonded abrasivematerial having peripheral teeth which are adapted to mesh in running involute-engagement with a cylindrical gear to be lapped, said teeth having a pressure angle varying progressively along the flanks, the tops and roots of said teeth beingtapered in one direction and the bases of said teeth being tapered in the opposite direction axially of the lapping member.

11. As an article of manufacture, a rotary gearshaped lapping member adapted to lap a gear conjugate therewith, said member having periphmedial normal line of rolling contact of the gear with a like mating gear, said lapping teeth being generated on a base cylinder and having the tops and the roots tapered in one direction and the bases tapered in the opposite direction axially of the lapping member.

13. As an article of manufacture, a rotary lapping member having the shape of an internal gear and being adapted to lap the teeth of a gear in rotary engagement therewith, said lapping member having teeth of bonded abrasive material conjugate to the gear teeth, and each of said lapping teeth having a pressure angle varying progressively in degree along each of the tooth flanks. n

14. The method of lapping a gear consisting of engaging said gear with a lap, which, when running in .mesh with said gear, has a medial line of rolling "contact with each successive tooth flank of said gear and abrades said tooth flank above and below said line of rolling contact, said line of rolling contact being disposed obliquely with reference to the normal medial line ofroll-j ing contact'of said tooth flank with a flank of a similar gear, and running said gear and said lap together first in one direction and then in the reverse direction.

15. The method of lapping a gear which comprises positioning the gear in meshing engagement with a conjugate gear-shaped lap whose axis lies in the same plane as the axis of said gear and is disposed obliquely relatively thereto and whose pressure angle varies progressively along each gear tooth flank, simultaneously positioning said gear in meshing engagement with a second conjugate gear-shaped lap whose axis lies in the same plane as the axis of said gear and is disposed obliquely relatively thereto and whose pressure angle varies progressively along each tooth flank but relatively in the opposite direction to that of said first mentioned lap, running said gear and said laps together while in said engagement first in-one direction of r0- tatidn and then in the reverse direction of rotation, and relatively moving said gear and each lap in a direction parallel to the axis of saidgear during said engagement.

16. The method of lapping a gear which comprises positioning the gear at one side in meshing engagement with a conjugate gear-shaped lap whose axis lies in the same. plane as the axis of said gear and is disposed obliquely relatively thereto and whose pressure angle varies progressively along each gear tooth flank, simulaneously positioning said gear at a diametrically opposite side in meshing engagement with a second conjugate gear-shaped lap whose axis liesv in the same plane as the axis of said gear and is disposed parallel to the axis of said first mentioned lap and .whose pressure varies progressively along each gear tooth flank but in the opposite direction to that of said first mentioned lap, running said gear and said laps together while in said engagement first in one direction of rotation with the laps acting respectively against opposite sides of the gear. teeth 

